Mr. Bachmayr has left the institute. This page is no longer maintained.
Research Topics
- Nonlinear approximation and adaptive methods
- High-dimensional partial differential equations
- Applications in quantum chemistry and in uncertainty quantification
News
- New preprint Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs (with V. Kazeev)
Research seminar series Mathematics of Computation
Upcoming Conferences
- Uncertainty quantification for complex systems: theory and methodologies, Isaac Newton Institute, Cambridge, Mar 5-16, 2018
- GAMM Annual Meeting 2018, Mar 19-23, Munich
- MoRePaS 2018, Apr 10-13, Nantes
- Numerical Analysis of Complex PDE Models in the Sciences, June 11-15, Erwin Schrödinger Institute, Vienna
Teaching
See teaching activities of the whole group.
Current Research Projects
Publications
Preprints
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Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs.
M. Bachmayr and V. Kazeev.
arXiv:1802.09062, 2018.
Also available as INS Preprint No. 1802.
BibTeX
arXiv
Journal Papers
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Kolmogorov widths and low-rank approximations of parametric elliptic PDEs.
M. Bachmayr and A. Cohen.
Mathematics of Computation, 86:701–724, 2017.
BibTeX
DOI
arXiv
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Parametric PDEs: Sparse or low-rank approximations?
M. Bachmayr, A. Cohen, and W. Dahmen.
IMA Journal of Numerical Analysis, 2017.
To appear.
BibTeX
DOI
arXiv
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Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients.
M. Bachmayr, A. Cohen, R. DeVore, and G. Migliorati.
ESAIM Math. Model. Numer. Anal., 51(1):341–363, 2017.
BibTeX
DOI
arXiv
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Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients.
M. Bachmayr, A. Cohen, and G. Migliorati.
J. Fourier Anal. Appl., 2017.
To appear.
BibTeX
DOI
arXiv
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Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients.
M. Bachmayr, A. Cohen, and G. Migliorati.
ESAIM Math. Model. Numer. Anal., 51(1):321–339, 2017.
BibTeX
DOI
arXiv
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Fully discrete approximation of parametric and stochastic elliptic PDEs.
M. Bachmayr, Albert, Cohen, D. Dũng, and C. Schwab.
SIAM J. Numer. Anal., 55:2151–2186, 2017.
BibTeX
DOI
arXiv
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Iterative methods based on soft thresholding of hierarchical tensors.
M. Bachmayr and R. Schneider.
Found. Comput. Math., 17(4):1037–1083, 2017.
BibTeX
DOI
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Adaptive low-rank methods for problems on Sobolev spaces with error control in L2.
M. Bachmayr and W. Dahmen.
ESAIM Math. Model. Numer. Anal., 50(4):1107–1136, 2016.
BibTeX
DOI
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Adaptive low-rank methods: problems on Sobolev spaces.
M. Bachmayr and W. Dahmen.
SIAM J. Numer. Anal., 54(2):744–796, 2016.
BibTeX
DOI
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Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations.
M. Bachmayr, R. Schneider, and A. Uschmajew.
Found. Comput. Math., 16(6):1423–1472, 2016.
BibTeX
DOI
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Adaptive near-optimal rank tensor approximation for high-dimensional operator equations.
M. Bachmayr and W. Dahmen.
Found. Comput. Math., 15(4):839–898, 2015.
BibTeX
DOI
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Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry.
M. Bachmayr, H. Chen, and R. Schneider.
Numer. Math., 128(1):137–165, 2014.
BibTeX
DOI
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Approximation of high-dimensional rank one tensors.
M. Bachmayr, W. Dahmen, R. DeVore, and L. Grasedyck.
Constr. Approx., 39(2):385–395, 2014.
BibTeX
DOI
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Integration of products of Gaussians and wavelets with applications to electronic structure calculations.
M. Bachmayr.
SIAM J. Numer. Anal., 51(5):2491–2513, 2013.
BibTeX
DOI
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Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation.
M. Bachmayr.
ESAIM Math. Model. Numer. Anal., 46(6):1337–1362, 2012.
BibTeX
DOI
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Iterative total variation schemes for nonlinear inverse problems.
M. Bachmayr and M. Burger.
Inverse Problems, 25(10):105004, 26, 2009.
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DOI
Thesis
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Adaptive Low-Rank Wavelet Methods and Applications to Two-Electron Schrödinger Equations.
M. Bachmayr.
PhD thesis, RWTH Aachen, 2012.
BibTeX
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Iterative total variation methods for nonlinear inverse problems.
M. Bachmayr.
Master's thesis, Johannes Kepler Universität Linz, 2007.
BibTeX
Other Reports
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Adaptive near-optimal rank tensor approximation for high-dimensional operator equations.
M. Bachmayr.
In Oberwolfach Report 39/2013, Mathematisches Forschungsinstitut Oberwolfach.
BibTeX
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Adaptivity and preconditioning for high-dimensional elliptic partial differential equations.
M. Bachmayr.
In Oberwolfach Report 24/2014, Mathematisches Forschungsinstitut Oberwolfach.
BibTeX
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Hyperbolic wavelet discretization of the electronic Schrödinger equation: Explicit correlation and separable approximation of potentials.
M. Bachmayr.
In Oberwolfach Report 33/2010, Mathematisches Forschunginstitut Oberwolfach.
BibTeX
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Kolmogorov widths and low-rank approximations of parametric elliptic PDEs.
M. Bachmayr.
In Oberwolfach Report 2/2015, Mathematisches Forschungsinstitut Oberwolfach.
BibTeX
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Space-parameter-adaptive approximation of affine-parametric elliptic PDEs.
M. Bachmayr.
In Oberwolfach Report 17/2017, Mathematisches Forschungsinstitut Oberwolfach.
BibTeX